Can't scale biezer curve object after editing object in Blender 2.8
You need to understand how vertices in curves work: they are defined by a center point, where the curve goes through, and two handles which can be on the same axis or not.

The handles define the direction of the curve while exiting the vertex and their easing, just like a keyframe in the Graph editor. The central point is just a positional reference, like a normal vertex in a mesh, so it doesn't have a scale (it's a point: it's a "0D" element). The reason why you can scale multiple centerpoints is that they behave like vertices in a mesh, so if you scale them up they increase their distance from the median point.

In this gif you can see that you can scale the vertex up if you select 2 of them or you scale it from another point (the 3D cursor in my case)